Metrics with Nonnegative Curvature on S^2xR^4

Details Metrics with Nonnegative Curvature on S^2xR^4 Metrics with Nonnegative Curvature on S^2xR^4

2010-10-27

arxiv.org/abs/1010.5738v1

Mathematics

Differential Geometry

Scientific paper

We study nonnegatively curved metrics on S^2xR^4. First, we prove rigidity theorems for connection metrics; for example, the holonomy group of the normal bundle of the soul must lie in a maximal torus of SO(4). Next, we prove that Wilking's almost-positively curved metric on S2xS3 extends to a nonnegatively curved metric on S^2xR^4 (so that Wilking's space becomes the distance sphere of radius 1 about the soul). We describe in detail the geometry of this extended metric.

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